Saudi Arabian club, Al-Ittihad, have emerged as front-runners in the race for Jared Borgetti's signature.
The cash-rich Saudis, who tried to sign him a year ago, have lined up a lucrative two-year contract and are prepared to pay Wanderers £500,000.
Allardyce is prepared to offload the 32-year-old Mexican, who has failed to command a regular first team spot with Wanderers, spending much of last season on the subs' bench, and has confirmed receiving a number of enquiries.
But he has stressed that he would only let him go if the deal was right for the club and for the player.
Borgetti has made it known he would prefer to stay at the Reebok, but wants more action.
"If I do not play regularly, the best option will be my exit," he said recently. "I've always been very disciplined but I have a limit and I believe I am not a man for the bench."
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